The Realm of the Nebulae

The universe is populated with galaxies -- some like
our own Milky Way, others very different. Recognizing other
galaxies and estimating their distances led astronomers to the
realization that the universe is expanding.

Topics

Distances to Other Galaxies

Galaxies and Their Environments

The Redshift

Dark Matter

Galaxy Formation

The Andromeda ``Nebula''

Distances to Other Galaxies

To determine if Andromeda was another ``island
universe'' -- a galaxy like the Milky Way -- we needed to find out
its distance. For this we had to find brighter objects which could
be used as standard candles. A special kind of star, known
as a Cepheid variable, turned out to be just what was
required.

Cepheid variables are giant stars. Instead of shining
steadily, they vary in brightness, following a regular
pattern. The time a variable star takes to go through one
cycle is known as its period.

Cepheid have a number of advantages as standard candles:

Easily recognized

Extremely luminous

Luminosities can be measured

Leavitt's Law: the Period-Luminosity Relationship

Leavett was studying Cepheid variable stars in the Large
Magellanic Cloud, a small satellite galaxy orbiting the Milky
Way. She noticed that the average brightness of these stars
was related to their periods. Because all these stars are
equally far away, this implied there was a relationship
between period and average luminosity.

No Cepheid variable was close enough for a parallax
measurement, but some were found in star clusters whose
distances could be measured by main-sequence fitting. This
enabled astronomers to determine the period-luminosity
relationship, and turn Cepheid variables into standard
candles.

The Distance to Andromeda

In 1924, Hubble found Cepheid variable stars in Andromeda. He
measured their periods and used the period-luminosity
relationship to determine their luminosities. Luminosities
and average brightnesses in turn yielded distances.

Andromeda turned out to be much further away than
anything associated with the Milky Way, 2.4 million light
years, or

dAnd = 736 kpc = 0.736 Mpc .

At this distance, Andromeda was about twice the size as the
Milky Way! With this, astronomers realized that the Milky Way
was just one of the countless galaxies scattered
about the universe.

NGC 1316: An Elliptical Galaxy

M32: A Nearby Elliptical Galaxy

Sextans A: A Small Irregular Galaxy in the Local Group

Galaxy Classification

Hubble and others sorted galaxies into several different
classes -- ellipticals, spirals, and irregulars -- on the
basis of their appearance.

Groups and Clusters

Galaxies like company. The Milky Way and Andromeda, together
with several dozen smaller galaxies, make up the local
group. The nearest big cluster of galaxies is the
Virgo Cluster (right), which contains about a
thousand galaxies!

Big, ``regular'' clusters like these are rich in
elliptical galaxies. Spiral galaxies are more often found in groups
and in ``irregular'' clusters.

The Hercules Cluster of Galaxies

Hercules contains a larger fraction spiral
galaxies than Virgo, and some of these galaxies are
colliding.

The Redshift

Even before the nature of galaxies was understood, it was
known that their spectra, while showing basically the
same patterns of lines as nearby stars and star-forming gas
clouds, tended to be shifted toward the red.

This shift follows a simple rule: the change in wavelength
Δλ is always a fixed fraction of
λ0, the wavelength measured locally.

This fraction is known as the redshift:

z = Δλ ⁄ λ0 .

Redshifts are due to relative velocity: other
galaxies are moving away from us at speeds
v = c z, where c is the speed of
light.

Redshift: An Example

The lines in this spectrum are all shifted by the same
factor; for example:

Line

λ

λ0

Δλ

z = Δλ ⁄ λ0

v = c z

(Å)

(Å)

(Å)

(km ⁄ sec)

Hβ

5009

4861

148

0.0304

9120

Hγ

4472

4340

132

0.0304

9120

The Expansion of the Universe

Plotting redshifts of galaxies against their distances, Hubble
found that each was proportional to the other:

v = H0d .

Modern measurements give

H0 = 72 km ⁄ sec ⁄ Mpc .

Hubble's discovery had two key implications. First,
it provides an easy way to estimate the distance to a galaxy: take a
spectrum, measure the redshift, and calculate d. Second; it
shows that the universe is expanding.

Was it Something We Did?

The Cartoon History of the Universe

The Universe Has No Center

Expansion from MW

Expansion from Galaxy 2

Expansion from Galaxy 3

Observed from MW

Observed from Galaxy 2

Observed from Galaxy 3

The expansion looks the same no matter where
we are: all observers see other galaxies moving away from their
galaxy, with speeds proportional to distances. The expansion of the
universe does not define a center.

The Universe Has No Edge

It's natural to think of a finite sphere of galaxies expanding
into nothingness. But there's no evidence the universe as an
edge -- looking further and further, we just see more and more
galaxies in all directions...

The Universe Has No Edge

It's natural to think of a finite sphere of galaxies expanding
into nothingness. But there's no evidence the universe as an
edge -- looking further and further, we just see more and more
galaxies in all directions...

From a mathematical point of view, it's much harder to
describe a finite universe like this one. The preferred
model of the universe is infinite in all directions.

The Universe Has An Age

The simplest assumption we can make is that the
galaxies move away from each other at constant rates. If that's
true, we can ask how long ago all galaxies were ``on top of each
other''.

Consider a galaxy now at a distance of
d = 100 Mpc; its speed away from us is

v = H0d =
(72 km ⁄ sec ⁄ Mpc)
× (100 Mpc) =
7200 km ⁄ sec .

Assuming the galaxy's speed has been constant, it
covered this distance in time

t

=

d

v

=

100 Mpc

7200 km ⁄ sec

=

3.09×1021km

7200 km ⁄ sec

=

4.29×1017sec

=

13.6 Gyr .

(The distance d actually cancels out of this
calculation, and you would get the same answer for any other
choice of d.)

13.6 Gyr is a reasonable estimate
for the age of the universe!

Dark Matter

The visible parts of galaxies turn out to be only a few
percent of the mass in the universe. Zwicky noticed this
while studying orbital speeds of galaxies in galaxy clusters.
If the visible stars were the only matter present, the
galaxies should orbit with speeds of about
100 km ⁄ sec.

In fact, the speeds were typically 10 times larger,
or about 1000 km ⁄ sec!
If galaxy clusters are held together by gravity, their
total masses have to be about 100 times the visible mass. In
other words, galaxies are only about 1% the mass of a
cluster.

Hot Gas in Galaxy Clusters

Hot gas (temperature T =
107 K) in galaxy clusters provides another
line of evidence for dark matter. This gas would easily
escape the feeble gravity of cluster galaxies; the gravity
required to hold it in place requires, again, about 100 times
the visible mass in the galaxies.

The amount of hot gas is about 10
times the mass in galaxies.
90% of the cluster's mass is still in an
unknown form!

Gravitational Lensing by Clusters

Another line of evidence is provided by
gravitational lensing, the bending of light by strong
gravitational fields. When we look at galaxy clusters, we see
images of background galaxies distorted into arcs. The amount of
mass required to do this is about the same amount required to
explain the speeds of cluster galaxies and retain the hot gas.

Galaxy Rotation Curves

The rotation of galaxies provides more evidence of dark
matter. If galaxies only contained visible matter, stars
orbiting at large radii R would follow Kepler's third
law, with orbital speeds

Rubin observed that the orbital speeds are roughly
constant, instead of inversely proportional to the square
root of the radius. This implies that each galaxy has a halo of
dark matter, probably roughly spherical, enveloping the visible
stars and gas.

What is This Dark Stuff?

We have a good idea of what the dark matter is
not.

Not stars -- we would see them

Not brown dwarfs -- microlensing would find them

Not black holes -- microlensing would find them

Not gas at any temperature -- we could detect that

Our best guess is that the dark matter is some kind
of sub-atomic particle. Like neutrinos, these particles must be
almost completely indifferent to ordinary matter. (Neutrinos were
actually a leading candidate for the dark matter, but it turns out
they can't provide the necessary mass.) The jury is still out on
the true nature of the dark matter.

Galaxy Formation

Dark matter determines how galaxies form. At early times,
mass was very smoothly distributed throughout the universe.
Gravity pulled the dark matter into clumps which grew by
merging with each other. Visible galaxies grew at the centers
of these clumps of dark matter.

Clustering of dark matter

This scenario predicts that galaxies can merge when
their parent clumps or halos of dark matter fall together.
Supporting this idea, we find examples of merging galaxies
throughout the universe.